This program computes the sum of the numbers between 1 and a given integer n. A problem well
known as 'Little Gauss'. Ask your preferred Internet search engine if you have not heard about 'Little Gauss'.
The program provides two solutions for the problem. First a brute force algorithm adding one number after the other. This version uses the internal HP-15C function ISG. Secondly the program provides the original formula found by Gauss:
n n(n + 1)
∑ k = ——————————
k=1 2
n, for which you want to compute the Gauss sum.
Due to the limitations of the ISG function, n must be less than 1000 when using this version.
| A | Little Gauss using built in function ISG |
| B | Little Gauss using the formula |
| 1 | Start of ISG sub program |
| 2 | Sub program to sum up the numbers |
| 3 | Set flag 9 (blinking) in case of error |
| 0 | Cumulated sum |
| 1 | Counter for ISG function |
| 9 | Flag 9 is set if the integer number is greater than 999 when using the ISG version. |
Line Code Mnemonic
000 { }
001 { 42 21 11 } f LBL A
002 { 9 } 9
003 { 9 } 9
004 { 9 } 9
005 { 43 30 8 } g TEST x<y
006 { 22 3 } GTO 3
007 { 42 34 } f REG
008 { 34 } x↔y
009 { 1 } 1
010 { 26 } EEX
011 { 3 } 3
012 { 16 } CHS
013 { 20 } ×
014 { 1 } 1
015 { 26 } EEX
016 { 5 } 5
017 { 16 } CHS
018 { 40 } +
019 { 44 1 } STO 1
020 { 42 21 1 } f LBL 1
021 { 42 6 1 } f ISG 1
022 { 22 2 } GTO 2
023 { 45 0 } RCL 0
024 { 43 32 } g RTN
025 { 42 21 2 } f LBL 2
026 { 45 1 } RCL 1
027 { 43 44 } g INT
028 { 44 40 0 } STO + 0
029 { 22 1 } GTO 1
030 { 42 21 3 } f LBL 3
031 { 43 4 9 } g SF 9
032 { 43 32 } g RTN
033 { 42 21 12 } f LBL B
034 { 36 } ENTER
035 { 36 } ENTER
036 { 1 } 1
037 { 40 } +
038 { 20 } ×
039 { 2 } 2
040 { 10 } ÷
041 { 43 32 } g RTN